Your 20minute "lay of the land" presentation should address the following points:

1. What is the problem?

Examples
Definition (input-output)
What would solution look like?
(Eg, "any X s.t. Y", or "an X s.t. Y which maximizes Z", or ..)

2. Why is the problem important? (ie, why should I care?)

Ie, if it was solved...

what would that make possible?
would the world be a happier place?
would I make a gazillion dollars?

3. Why isn't this task trivial?

(Ie, explain why I can't just solve it in my sleep...)
Here, it may be useful to point to

theoretical results (eg, "task is NP-hard")
... coupled with an argument for why the specific tasks that people address,
will be large, and be difficult (ie, not a special case).
mention real-world situation
(eg, "dozens of PhDs in CompanyX are working full time on this...")
present a well-chosen example to give some insights on the complexities here
-- an example is one that is easy to state, but not obvious how to solve.
(Eg, show that obvious solutions don't work)

4. The people (researchers, developers, technicians) who really need to solve this problem: What do they do?

This should be a quick survey of the TYPES of techniques

do companies/people really commit the resources to find the exact solutions to general, hard problems?
are there special cases where exact solutions are possible?
are there good approximations?
are there usually-effective probabilistic/stochastic algorithms?
...

(Part 4 is the "lay of the land" portion; this should be the bulk of the presentation -- say 15 minutes.)

Your final presentation - during the last week of the course -- should quickly summarize 1-4, then spend most of the time giving the actual results.

Some other comments, about presentations in general:

People are uni-processors: if they are reading, they are NOT listening.
Therefore, it makes sense to write as LITTLE material on your slides as possible.
- Avoid complete sentences; use Bullets!
- Use LARGE fonts

Give a simple examples FIRST, before giving the formal definitions, theorems, etc.
Then perhaps use that example to "instantiate" the definitions, etc.
(Don't worry: people typically do an amazingly great job of generalizing from such examples.)

Try to avoid technical terms, if at all possible. (Or at least give a simple example of the idea.)